A non-perturbative open-shell theory for ionisation potential and excitation energies using HF ground state as the vacuum

Time-Dependent Multireference Coupled-Cluster Method (TDMRCCM) for the Bath-Dynamics in System-Bath Approach to Nonadiabatic Dynamics

The time-dependent multireference coupled-cluster method (TDMRCCM) fits well in the scheme of the system-bath separation used to study the nonadiabatic dynamics. In TDMRCCM, a projection operator is defined as one that projects the full Hilbert space onto the space spanned by the collection of system degrees of freedom, called the model space. The inverse of this projection operator is a wave operator that acts on the model space and takes its projection back to the full wave function. This wave operator is defined as an exponential of the excitation terms and, hence, can be expanded into a Taylor series, which we have truncated in this work at the second-order of excitations. The attraction of using TDMRCCM for describing the bath dynamics is due to the exponential nature of the ansatz used in the method, which makes it possible for the higher-order excitations to be absorbed by the lower-order terms, even upon truncating the series. This improves the accuracy of the numerical calculations using TDMRCCM as an approximation for the bath-mode dynamics in the system-bath framework for nonadiabatic dynamics. We present the theoretical details of TDMRCCM and the numerical results for implementing this method to study the dynamics in the butatriene cation.

Benchmark Study of the Electronic States of the LiRb Molecule: Ab Initio Calculations with the Fock Space Coupled Cluster Approach

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene

We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.

Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree-Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.

Extension of the Fock-space coupled-cluster method with singles and doubles to the three-valence sector

The single-reference coupled-cluster method has proven very effective in the ab initio description of atomic and molecular systems, but its successful application is limited to states dominated by a single Slater determinant, which is used as the reference. In cases where several determinants are important in the wave function expansion, i.e., we have to deal with nondynamic correlation effects, a multi-reference version of the coupled-cluster method is required. The multi-reference coupled-cluster approaches are based on the effective Hamiltonian formulation providing a two-step procedure, in which dynamic correlation effects can be efficiently evaluated by the wave operator, while nondynamic correlation contributions are given by diagonalization of the effective Hamiltonian in the final step. There are two classical multi-reference coupled-cluster formulations. In this paper, the focus is on the so-called Fock-space coupled-cluster method in its basic version with one- and two-particle operators in the exponent. Computational schemes using this truncation of the cluster operator have been successfully applied in calculations in one- and two-valence sectors of the Fock space. In this paper, we show that the approach can be easily extended and effectively employed in the three-valence sector calculations.

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Development of a relaxation-inducing cluster expansion formalism for treating strong relaxation and correlation effects

We present in this paper a comprehensive account of an explicitly spin-free coupled cluster theory for treating energy differences of open-shell states relative to a closed-shell ground state, where the open-shell states of interest are dominated by a few simple configuration state functions. We develop a valence-universal coupled cluster formalism to achieve this via a novel cluster expansion ansatz for the valence part of the wave operator, where the orbital relaxation and the correlation relaxation accompanying ionization/excitation from the ground state are taken care of to all orders in compact, efficient, and explicitly spin-free manner. The essential difference of our proposed ansatz from the ordinary and the normal-ordered cluster ansatz in vogue is that (a) we allow the valence cluster operators to be connected among themselves with spectator valence lines only and (b) we use suitable combinatoric factors accompanying powers of cluster operators thus connected, which are equal to the number of ways the operators can be joined, leading to the same excitation (the automorphic factor). We emphasize that such an ansatz does not generate terms (diagrams) with chains of cluster operators joined among themselves via spectator lines only. Barring only a few, almost all the terms in the working equations determining the cluster amplitudes involve contraction of the Hamiltonian with the cluster operators via at least one nonspectator line, leading to what we call a "strongly connected" series. The structure of the working equation is remarkably similar to the single-reference closed-shell equation, with a few additional terms. The presence of contractions among cluster operators via spectator lines introduces the additional physical effects of orbital and correlation relaxation using low-body cluster operators. As an illustrative application of the new multireference coupled cluster (CC) theory, we consider in this paper computation of ionization potentials (IPs) of one-valence problem with only one active orbital. The numerical applications are made for both the core- and the inner- and outer-valence IPs for several molecular systems. The numerical values demonstrate the superiority of the relaxation-inducing CC theory, as compared to the normal-ordered ansatz.

The Fock-Space Coupled-Cluster Method in the Calculation of Excited State Properties

Our recently developed intermediate Hamiltonian Fock-space coupled-cluster (FS-CC) method with singles and doubles is applied to calculation of equilibrium geometries, harmonic frequencies and adiabatic excitation energies for some excited states of N2 and CO. Due to the intermediate Hamiltonian formulation, which provides a robust computational scheme for solving the FS-CC equations, and the efficient factorization strategy, relatively large basis sets and reference spaces are employed permitting a comparison of calculated properties with experimental data.